The Heston Model and Its Extensions in VBA.

Intro -- The Heston Model and Its Extensions in VBA -- Contents -- Foreword -- Preface -- Acknowledgments -- About This Book -- VBA Library for Complex Numbers -- 1 The Heston Model for European Options -- Model Dynamics -- The Heston European Call Price -- Dividend Yield and the Put Price -- Consolidating the Integrals -- Black-Scholes as a Special Case -- Conclusion -- 2 Integration Issues, Parameter Effects, and Variance Modeling -- Remarks on the Characteristic Functions -- Problems with the Integrand -- The Little Heston Trap -- Effect of the Heston Parameters -- Heston Terminal Spot Price -- Effect of Correlation and Volatility of Variance -- Comparison with Black-Scholes Prices -- Heston Implied Volatility -- Variance Modeling in the Heston Model -- Variance Swap -- Dupire Local Volatility -- Local Volatility with Finite Differences -- Approximate Local Volatility -- Numerical Illustration of Local Volatility -- Implied Volatility -- Moment Explosions -- Bounds on Implied Volatility Slope -- Conclusion -- 3 Derivations Using the Fourier Transform -- Derivation of Gatheral (2006) -- Attari (2004) Representation -- Carr and Madan (1999) Representation -- Bounds on the Damping Factor and Optimal Value -- Optimal Damping Factor -- Numerical Implementation and Illustration -- The Representation for Puts -- The Representation for OTM Options -- Generalization of the OTM Representation -- Conclusion -- 4 The Fundamental Transform for Pricing Options -- The Payoff Transform -- The Fundamental Transform and the Option Price -- The Fundamental Transform for the Heston Model -- The Call Price Using the Fundamental Transform -- Option Prices Using Parsevals Identity -- Parsevals Identity and the Option Price -- Parsevals Identity for the Heston Model -- Contour Variations and the Call Price -- Volatility of Volatility Series Expansion -- Conclusion.

5 Numerical Integration Schemes -- The Integrand in Numerical Integration -- Newton-Cotes Formulas -- Midpoint Rule -- Trapezoidal Rule -- Trapezoidal Rule for Double Integrals -- Simpsons Rule -- Simpsons Three-Eighths Rule -- Gaussian Quadrature -- Gauss-Laguerre Quadrature -- Gauss-Legendre Quadrature -- Gauss-Lobatto Quadrature -- Gaussian Quadrature for Double Integrals -- Integration Limits, Multidomain Integration, and Kahl and Jäckel Transformation -- Illustration of Numerical Integration -- Fast Fourier Transform -- Fractional Fast Fourier Transform -- Conclusion -- 6 Parameter Estimation -- Estimation Using Loss Functions -- The Nelder-Mead Algorithm in VBA -- Starting Values -- Speeding Up the Estimation -- Differential Evolution -- Maximum Likelihood Estimation -- Risk-Neutral Density and Arbitrage-Free Volatility Surface -- Conclusion -- 7 Simulation in the Heston Model -- General Setup -- Euler Scheme -- Milstein Scheme -- Implicit Milstein Scheme -- Transformed Volatility Scheme -- Balanced, Pathwise, and IJK Schemes -- Quadratic-Exponential Scheme -- Alfonsi Scheme for the Variance -- Moment-Matching Scheme -- Conclusion -- 8 American Options -- Least-Squares Monte Carlo -- The Explicit Method -- Beliaeva-Nawalkha Bivariate Tree -- Trinomial Tree for the Variance -- Trinomial Tree for the Stock Price -- Combining the Trinomial Trees -- Implementation in VBA -- Medvedev-Scaillet Expansion -- Medvedev-Scaillet for Black-Scholes -- Medvedev-Scaillet for Heston -- Chiarella and Ziogas American Call -- Early Exercise Boundary Approximation -- The American Call Price -- Estimating the Early Exercise Boundary -- Conclusion -- 9 Time-Dependent Heston Models -- Generalization of the Riccati Equation -- Bivariate Characteristic Function -- Linking the Bivariate CF and the General Riccati Equation -- Mikhailov and Nögel Model -- Elices Model.

Benhamou-Miri-Gobet Model -- Constant Parameters -- Piecewise Constant Parameters -- Black-Scholes Derivatives -- Conclusion -- 10 Methods for Finite Differences -- The PDE in Terms of an Operator -- Building Grids -- Finite Difference Approximation of Derivatives -- Boundary Conditions for the PDE -- The Weighted Method -- Explicit Scheme -- ADI Schemes -- Conclusion -- 11 The Heston Greeks -- Analytic Expressions for European Greeks -- Delta, Gamma, Rho, Theta, and Vega -- Vanna, Volga, and Other Greeks -- Finite Differences for the Greeks -- Numerical Implementation of the Greeks -- Greeks under the Attari and Carr-Madan Formulations -- Greeks under the Lewis Formulations -- Greeks Using the FFT and FRFT -- American Greeks Using Simulation -- American Greeks Using the Explicit Method -- American Greeks from Medvedev and Scaillet -- Conclusion -- 12 The Double Heston Model -- Multidimensional Feynman-Kac Theorem -- Double Heston Call Price -- Double Heston Greeks -- Parameter Estimation -- Simulation in the Double Heston Model -- Simulation of the Stock Price -- Euler Scheme for the Variance -- Alfonsi Scheme for the Variance -- Zhu Scheme for the Transformed Variance -- Quadratic-Exponential Scheme -- American Options in the Double Heston Model -- Conclusion -- Bibliography -- About the Website -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.